Big Data-driven, big data-driven, or big-data driven

Some authorities (such as IBM and Wikipedia) say that “big data” should not be capitalised, while others say it should be capitalised as “Big Data”.

Logically, it would be capitalised only if it were a proper noun, that is, if it identified a unique individual. For example, “the Internet” refers to the global internet, of which there is only one, so it is capitalised. Big data does not really seem to be like that. In any technical usage, it refers to the use of very large databases, and should therefore be a common noun.

In the popular imagination, however, all instances of big data coalesce into a monstrous global conspiratorial network of databases, called Big Data. It is akin to Deep State.

So, it seems to me that “big data” should be used in any sober context, and “Big Data” reserved for conspiracy theories untethered from objective reality.

But ... in a proofreading context I would have to correct “a Big Data-driven project” to “a big data-driven project”, which is ambiguous as it could mean either “a big project that is driven by data” or “a project that is driven by big data”.

Well, like you said in your post, it really depends on the context. For big data-driven project, I would say that is a big project that is data-driven. However, I would refer to a big-data driven project as a project driven by big data. You’re right though; the context really does matter, and the phrasing is also quite ambiguous.